CAT 2020 Quant Question [Slot 1] with Solution 19

Question

If a, b and c are positive integers such that ab = 432, bc = 96 and c < 9, then the smallest possible value of a + b + c is

  1. 56
  2. 59
  3. 49
  4. 46
Option: 4
Solution:

Given \(ab = 432,bc = 96\) and \(c < 9\)

To find the minimum value for \(a + b + c,\) the two larger numbers should be as close as possible.

The closest combination whose product is 432 is \(18 \times 24\). For \(b = 24,\) we get \(c = 4\) and \(a = 18\).

Hence the least value for \(a + b + c = 46\).

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CAT 2020 Quant questions with Solutions